microeconomics. question 4

4. _ a. 2/3 1 I Let the production function be f (2:1, :52) := 302:1 582/2 for all nonnegative (:31, 932). At any input bundle (3:1, 3:2), the marginal product of input 1 is equal to __________________ , and the marginal product of input 2 is equal to _________________ . At the input bundle (3:1,:52) = (2,3), the slope of the isoquant (level surface of the production function) at this bundle is equal to _________________ . Suppose that the price for input 1 is $10 and that for input 2 is $30, and that the rm needs to produce an output quantity 3; for some parameter y > 0. Then i. the slope of the isoquant at the cost-minimizing input bundle is equal to ____________ (the answer should be a real number) ii. the cost-nnimizing input bundle to produce output quantity 3; is to set $1 = _ __ _______ _ __ ______ __ __ and $2 = _________________________________ (the answers should be mathematical expressions of 3;) iii. the cost to produce output quantity y is equal to _ ____ _ __ __ ____ _ __ __ ___ __ (the answer should be a mathematical expression of y) . For any t > 1, f(t:r1,t;t2) = tf(9:1,a:2) where a = ______________ [the answer should be a real number], hence f(ta:1,ta:2) ______________ (>,